a) These ramp dimensions do not meet the ADA guidelines.
b) A measurement that would meet the guidelines is the ramp starting 39 feet away, with a height of 3 meters.
What is a slope?The slope of a situation is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
For the ramp in this problem, we have that the vertical change and the horizontal change are given as follows:
The vertical change is of: 3 feet.The horizontal change is of: 15 feet.The ratio between the vertical change to the horizontal change is of:
3/15 = 1/5.
Which is greater than 1/12, hence the ramp does not meet the ADA guidelines.
If the horizontal change was 13 times the vertical change, it would meet the ratio, hence a possible measurement is of:
3 feet vertical.39 feet horizontal.As the ratio would be of:
3/39 = 1/13 < 1/12.
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a person can play 1/6 of a song in 1/3 of a minute.
how many minutes does it take the person to play the whole song at once at this rate?
Answer:
2 minutes for a whole song.
Step-by-step explanation:
Given that,
→ (1/6) song = (1/3) minutes
Parts of whole song is,
→ (1/6) × 6 = 1
Then the required minutes taken to play whole song will be,
→ x/6 = 1/3
→ x = (1/3) × 6
→ x = 6/3
→ [ x = 2 min ]
Hence, 2 minutes for a whole song.
In the recent year, 51.9 billion aluminum cans were recycled. About how many cans per week is this?
The number of cans that are recycled is approximately 1 billion cans in 1 week.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
Given that 51.9 billion aluminum cans were recycled.
Therefore, the rate of recycled the can is;
51.9 billion / 1 year
We know that 1 year has 52 weeks
Then
51.9 billion / 1 year x 1 year / 52 weeks
= 51.9 (1) billion / 1 (52 ) weeks
= 51.9 billion/ 52 weeks
= 1 billion/ 1 week
Hence, the number of cans that are recycled is approximately 1 billion cans in 1 week.
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What sequence equation would represent this graph?
Equation of the given data y = 1750x -20,000 and graph of the equation is attached.
As given in the question,
Data of the table :
Year : 1 2 3 4 5
Investment : $20,000 $21,750 $23,500 $25,250 $27,000
(x₁, y₁) = ( 1, 20,000)
(x₂, y₂) = ( 2, 21,750)
Equation of the given graph is :
( y - 20,000)/ (x -1) = (21,750 - 20,000)/ (2 -1)
⇒ ( y - 20,000)/ (x -1) = 1750
⇒ y = 1,750x -18,250
Graph of the equation y = 1,750x -18,250 s represented by the graph.
Graph is attached.
Therefore, equation of the given data y = 1750x -20,000 and graph of the equation is attached.
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The graph of the absolute value parent function, f(x) = lxl, is stretched horizontally by a factor of 6 to creator the graph of g(x). What function is g(x)?
The function g(X) will be of the form g(x) = |x/6| ,when stretched by a factor of 6.
The function is f(x)=|x| .
We know that for transformation of a function of the form horizontal stretch by a factor of 'a' is given by the g(x)= f(x/a)
So in this given function the horizontal stretch is by a factor of 6.
Therefore g(x) = f(x/6)
or, g(x) = |x/6|
In the graph attached the green represents the function f(x) while the red represents the function g(x).
A function transformation either "moves," "resizes," or "reflects" the graph of anything similar to the parent function. The following are the three main types of function transformations:
Dilation is the only one of these changes that modifies the size of the original shape; the other two just change its location.
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please can someone solve this and tell me how at the end, it's gives -2 alpha beta instead of +2 alpha beta
I need answers ASAP pleeeeaase!!!!!
The value for the given expression [tex]\alpha ^{2} + \beta ^{2}[/tex] will be [tex](\alpha +\beta )^{2}-2\alpha \beta[/tex].
What are Algebraic Identities?
Algebraic identities are algebraic equations that hold true for any value of each of their variables. In factoring polynomials, they are also used.
As we know, [tex](a+b)^{2} = a^{2} +2ab + b^{2}[/tex] then,
For the given question, [tex](\alpha +\beta )^{2} = \alpha ^{2} +2\alpha \beta + \beta ^{2}[/tex]
Now, subtracting [tex]2\alpha \beta[/tex] on both sides then, we get
or, [tex](\alpha +\beta )^{2}-2\alpha \beta = \alpha ^{2} +2\alpha \beta + \beta ^{2}-2\alpha \beta[/tex]
or, [tex](\alpha +\beta )^{2}-2\alpha \beta = \alpha ^{2} + \beta ^{2}\\[/tex]
or, [tex]\alpha ^{2} + \beta ^{2}=(\alpha +\beta )^{2}-2\alpha \beta[/tex]
That's how the value [tex]-2\alpha \beta[/tex] comes.
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a standard deck of 52 cards is acquired. for those who do not know, a deck of cards contains 4 suits (hearts, diamonds, clubs, and spades). hearts and diamonds are red, clubs and spades are black. there are 13 denominations of cards (2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king, and ace). if you select two cards (without replacement), what is the probability that you select a black card and a red card?
The probability that you select a black card and a red card is 26/51 as per the condition mentioned "choosing two cards (without replacement )".
What is probability?The area of mathematics known as probability studies potential outcomes of events as well as their relative probabilities and distributions. Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.
Here,
Since we have not mentioned the order,
so it can black-red or red-black,
=26/52*26/51+26/52*26/51
=2*26/52*26/51
=26/51
Assuming you choose two cards (without replacement), there is a 26/51 chance that you will choose a black card and a red card.
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Graph the following features:
Y-intercept = -1
Slope = -2
The line that has a slope of -2 and a y-intercept of -1 is shown in the graph below.
What is the Equation of a Line in Slope-intercept Form?An equation of a line in slope-intercept form that is expressed as y = mx + b, can be graphed if we know the value of the slope (m), and the value of the y-intercept (b).
We are given the following:
Slope of a line (m) = -2Y-intercept of the line (b) = -1To write the equation of the line in slope-intercept form, substitute m = -2 and b = -1 into y = mx + b:
y = -2x - 1
This means that the rise/run of the line, which is the slope, to be graphed would be equal to -2 while the line will intercept the y-axis at point -1, because the y-intercept given is -1.
The line with the stated features are shown in the graph below.
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Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.
y = 90(1.02)
The exponential equation represents an exponential growth because the rate of decay is 1.02 which is greater than 1.
y = 90(1.02)^x
The general form equation is:
y(x)= a(1+r)^x such that r is the decay percent.
on comparing,
1 + r = 1.02
r = 1.02 - 1
r = 0.02
converting into percent
r = 0.02 * 100
r = 2%.
Hence the exponential growth is 2%.
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There are 10 girls and 20 boys in a class.
The class has a test.
The mean mark for all the class is 70
The mean mark for all the boys is 62
Work out the mean mark for the girls.
Answer:
86
Step-by-step explanation:
mean is calculated as
mean = [tex]\frac{sum}{count}[/tex]
given mean mark for class of 30 is 70 , then
[tex]\frac{sum}{30}[/tex] = 70 ( multiply both sides by 30 )
sum = 2100
given the mean mark for 20 boys is 62, then
[tex]\frac{sum}{20}[/tex] = 62 ( multiply both sides by 20 )
sum = 1240
the sum for the 10 girls is then 2100 - 1240 = 860
then mean score for the 10 girls is
mean = [tex]\frac{860}{10}[/tex] = 86
A number is raised to the third power, then subtracted from 15 to get 7. What is the number squared?
Answer:
x=22
Step-by-step explanation:
Let the unknown number be x
:- the power of x = x³
From the question
x³-15=7 and x²
x³=7+15
x³ * x²= 22
x= 22
A container with 3½ liters of weed killer can spray of a lawn. How many liters would it
take to spray 1 entire lawn?
The amount a container would take to spray 1 entire lawn is 7 litres.
Given that a container with 3½ liters of weed killer can spray 1/2 of a lawn.
We want to find the amount of liters to take a spray 1 entire lawn.
3½ liters of weed killer can spray 1/2,
liters take to spray 1 lawn is 3½/1/2=7 liters
Hence, the amount of liters it would take to spray 1 entire lawn when a container with 3½ liters of weed killer can spray of a lawn is 7 liters.
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Wesley is baking three pumpkin pies. He will use a total of 5 1/4 quarts of pumpkin for the pies. If each pie contains the same amount of pumpkin, how many cups of pumpkin would each pie contain?
Answer:
Lol
Step-by-step explanation:
k
The equation of line k is y+2=-6(x-7).line l includes the point (-6,8) and is perpendicular to line k. What is the equation of line l?
The equation of line [L] would be y = (1/6)x + 9.
What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
We have a equation of line [k] is y + 2 = -6(x - 7). Line [L] includes the point (-6,8) and is perpendicular to line k.
We have the equation of line [K] as -
y + 2 = - 6(x - 7)
y = - 6(x - 7) - 2
y = - 6x + 42 - 2
y = - 6x + 40
Slope of line [L] will be -
m[L] = 1/6
Assume the equation to be -
y = (1/6)x + c
Line [L] includes the point (-6, 8), so we can write -
8 = (1/6) x (- 6) + c
8 + 1 = c
c = 9
So, the equation will be -
y = (1/6)x + 9
Therefore, the equation of line [L] would be y = (1/6)x + 9.
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according to the almanac of questionable statistics, vol 4 (2012), the probability of a mass squirrel uprising in any given year is 0.47 and the probability that cats and dogs will sign a peace treaty allowing them to live together peacefully in any given year is 0.61. if we presume that these two events are independent, what is the probability of both happening next year?
If the two events described in the questions are independent events, the probability of both happening next year is 28.67%.
Independent events refer to events whose occurrence is not interdependent. In other words, if the probability of occurrence of event A is not influenced by the probability of occurrence of event B, then A and B are independent events. Mathematically, independent events are represented as P(A│B) and is calculated by multiplying the individual probabilities of the two events. The formula of probability of two independent events is:
P(A│B) = P(A)*P(B)
Hence,
P(A│B) = 0.47*0.61
P(A│B) = 0.47*0.61
P(A│B) = 0.2867
The probability of two events happening next year is 28.67%.
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You visit the Grand Canyon and drop a penny off the edge of the cliff. The distance the penny will fall is 32ft for the first second, 62ft the next second, 92ft the third second, and so on. How far will the penny have traveled after 7 seconds?
Answer:
212 feet fallen after 7 seconds
Step-by-step explanation:
You visit the Grand Canyon and drop a penny off the edge of the cliff. The distance the penny will fall is 32ft for the first second, 62ft the next second, 92ft the third second, and so on. How far will the penny have traveled after 7 seconds?
if 32 ft for 1 second
if 62 ft for 2 second
if 92 ft for 3 second
We see that the penny from second 1, falls an addition 30 ft/s.
equation: 32 + 30 (t - 1)
when t = 7 seconds:
32 + 30 (7 - 1)
32 + 30 (6)
32 + 180
= 212 feet fallen after 7 seconds
750 people go on a coach trip
each coach can hold 50 people
How many coaches are needed
Answer:
15 coaches
Step-by-step explanation:
750 people go on a coach trip each coach can hold 50 people How many coaches are needed?
750/50 = 15 coaches
Answer:
Answer:750÷50 = 15
The answer is 15.
Because 750 people are going in a coach trip and each coaches can hold 50 people.
Helpppppppssssss ejejnee
Answer:
Step-by-step explanation:
Arithmetic Sequence
Answer:
(a) Arithmetic Sequence
Step-by-step explanation:
You want to know if the graph of a straight line represent an arithmetic, geometric, or neither sequence.
Arithmetic sequenceAn arithmetic sequence is characterized by a common difference between terms that are 1 unit apart. A graph of an arithmetic sequence is points that lie on a straight line.
The graph shows an Arithmetic Sequence.
__
Additional comment
A graph of a geometric sequence would show points that lie on an exponential curve.
A
If m ZABD = 75° and m/ABC = 40°,
then mZCBD = [?]°
We see BC is in the middle of the lines AB and BD, therefore mABC + mCBD = mABD.
We're given mABD = 75, mABC = 40.
Therefore, mCBD = mABD - mABC = 75 - 40 = 35.
Answer:
∠CBD = 35°
Step-by-step explanation:
We are told in the question that m∠ABD = 75° and m∠ABC = 40°. We are then asked what the value of m∠CBD is.
As we can see from the diagram, ∠ABD is made up of the angles ABC and CBD. Therefore:
∠ABD = ∠ABC + ∠CBD
⇒ 75° = 40° + ∠CBD
⇒ 75° - 40° = 40° + ∠CBD - 40° [
⇒ 35° = ∠CBD
∴ ∠CBD = 35°
XR is tangent to circle O at point X. IfmXY = 110°, find m/YXR.
X
O
R
F
Y
D
The measure of ∠ YXR is 55 degrees.
Given that:-
m∠ XOY = 110 degrees
XR is a tangent to circle O at X.
We have to find the measure of ∠ YXR.
Draw the radii XO and OY to form the isosceles triangle XOY.
We know that the radius of the circle is perpendicular to the tangent.
Hence, ∠OXR = 90 degrees.
Consider the triangle XOR, we know that XO and OY are the radii of the triangle and hence equal.
Let, ∠ OXY = OYX = x
Hence,
110 + x + x = 180 degrees
2x = 70 degrees
x = 35 degrees
Now, we know that,
∠ OXR = ∠ OXY + ∠ YXR
90 = 35 + ∠ YXR
∠ YXR = 90 - 35 = 55 degrees.
∠ YXR = 55 degrees.
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round off to round off 36 to the nearest day
what is the probability that 5 hearts are chosen if 8 cards are chosen from a well-shuffled deck of 52 playing cards?
The probability that 5 hearts are chosen if 8 cards are selected from a well-shuffled deck of 52 playing cards is 0.0156296302.
The number of choosing 8 cards out of 52 is = ⁵²C₈
Number of ways of choosing 5 cards of heart out of 13 cards and 3 out of remaining 39 cards = ¹³C₅ × ³⁹C₃
Probability of choosing 5 hearts = ¹³C₅ × ³⁹C₃ / ⁵²C₈
= 1287 ×9139 / 752538156
= 11761893 / 752538156
= 0.0156296302
A basic 52-card deck consists of 13 ranks in each of the four French suits: clubs, diamonds, hearts, and spades. Each card includes three court cards (face cards), King, Queen, and Jack, as well as reversible (double-headed) images. Each card also contains ten numeral cards or pip cards, from one to ten.
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It cost Hassan $5.31 to send 59 text messages. How much does each text cost to send?
Each text will cost Hassan $0.09
What is rate ?A rate is a special ratio in which the two terms are in different units. It can also be defined as the amount of money that is charged for goods or services. For example, if a 12 malt can of costs 69¢, the rate is 69¢ for 12 malt. Then 1 malt will cost ¢69/12.
Similarly $5.31 is the cost of 59 text messages
Therefore a text message will cost $5.31/12=$0.09
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Niecy has Nine-fourteenths of a cup of pears and Three-fourteenths of a cup of mangos. She combines the fruit in one container.
How many cups of fruit does Niecy have in the container?
Three-fourteenths
Six-fourteenths
StartFraction 12 over 14 EndFraction
StartFraction 27 over 14 EndFraction
When Niecy combines the fruit she will have a total of Start Fraction 12 over 14 End Fraction
How to calculate sum of fruits Niecy will haveinformation form the question
Niecy has Nine-fourteenths of a cup of pears
Three-fourteenths of a cup of mangos
The problem is faced with addition of fractions
writing out the fractions in figures gives
Niecy has Nine-fourteenths of a cup of pears = 9 / 14
Three-fourteenths of a cup of mangos = 3 / 14
Addition of the fraction is done as follows
= 9 / 14 + 3 / 14
= (9 + 3) / 14
= 12 / 14
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Need the answer for this
Answer:
x = 41.5
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180°
sum the 3 angles and equate to 180
2x + 9 + x + 13 + x - 8 = 180 , that is
4x + 14 = 180 ( subtract 14 from both sides )
4x = 166 ( divide both sides by 4 )
x = 41.5
⇒The sum of the interior angles of a triangle is 180°
⇒Meaning (2x+9)°+(x-8)°+(x+13)°=180°
⇒Simplify the above equation to find the value of x.
⇒[tex]2x+x+x+9-8+13=180\\4x+14=180\\4x=180-14\\4x=166\\\frac{4x}{4} =\frac{166}{4} \\x=41.5[/tex]
∴ x=41.5
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The equation of the parabola with the vertex (3,5) in the form of f(x)=a(x-h)^2+k is f(x)=7(x-3)^2+5.
In the given question we have to find the equation of parabola in the form of f(x)=a(x-h)^2+k
The given function is f(x)=7x^2.
The given vertex = (3,5)
The equation of the parabola with the vertex of (h,k) is
y=a(x-h)^2+k
On comparing we get; a=7, h=3, k=5
Now putting the value
f(x)=7(x-3)^2+5
Hence, the equation of the parabola with the vertex (3,5) in the form of f(x)=a(x-h)^2+k is f(x)=7(x-3)^2+5.
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The following sets of ordered pairs represent relations from the set X to the set Y. Which one is a function?
A (3, 4), (3, 5), (3, 6), (3, 7)
B (2, 5), (2, 8), (3, 7), (3, 9)
C (1, -1), (0, 0), (1, 1), (4, 2)
D (0, 0), (1, 1), (4, 2), (9, 3)
The set of ordered pairs that is a function is (d) (0, 0), (1, 1), (4, 2), (9, 3)
How to determine the ordered pair that is a function?The list of options represents the given parameter
As a general rule, for an ordered pair to be a function;
The y values on the ordered pair must point to different x values
In (a) the y values 4, 5, 6 and 7 have the same x value of 3
So, it is not a function
In (b) the y values 5 and 8 have the same x value of 2
So, it is not a function
In (c) the y values -1 and 1 have the same x value of 1
So, it is not a function
In (d) all the y values have different x values
So, it is a function
Hence, the ordered pair that is a function is (d)
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a triangular flower garden in the front of the house to increase curb appeal she has 12 square feet of space to work with . What are 2 possible dimensions for her flower garden ? Sketch a picture and justify your answer mathematically .
The possible dimension of the triangular garden assuming it to be a right-angle triangle is (12,2),(8,3), and (4,6).
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The area of a triangle is given as (1/2) × base × height.
The given area of the triangle = 12 feet².
Thus,
12 = (1/2) × base × height
Base × height = 12 × 2
Base × height = 24
The combination of two quantities gives 24 by multiplying will be (12,2),(8,3), and (4,6).
For example, the triangle with dimensions (4,6) is attached below.
Hence "The possible dimension of the triangular garden assuming it to be a right-angle triangle is (12,2),(8,3), and (4,6)".
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Find the error in the calculations below, if there is one:
Line (1): 4x³ + 2x² − 6x +3
Line (2): = 2x²(2x + 1) − 3(2x + 1)
Line (3): = 2x²(2x + 1) + ( − 3)(2x + 1)
Line (4): = (2x² − 3)(2x + 1)
Line 1 4x³ + 2x² − 6x +3 is having error.
Line 1.
4x³ + 2x² − 6x +3
Line 2.
= 2x²(2x + 1) − 3(2x + 1)
= 4x³ + 2x² - 6x - 3
Line 3.
= 2x²(2x + 1) + ( − 3)(2x + 1)
= 4x³ + 2x² - 6x - 3
Line 4.
= (2x² − 3)(2x + 1)
= 4x³ + 2x² - 6x - 3
expect line 1 remaining all three are equal.
Therefore Line 1 4x³ + 2x² − 6x +3 is having error.
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What is the m (See image)
From the given figure, m∠AEB = (3x + 54)° and m∠DEC = (7x -30)°, then the measure of angle AEB is equal to 117°.
As given in the question,
For the given figure,
Two lines AC and BD intersect each other at point E.
Measure of angles in the form of x is given as :
m∠AEB = (3x + 54)°
m∠DEC = (7x -30)°
∠AEB and ∠DEC are vertically opposite angles.
⇒m∠AEB = m∠DEC
⇒ (3x + 54)°= (7x -30)°
⇒ 7x - 3x = ( 54 + 30 )°
⇒ 4x = 84°
⇒ x = 21°
Hence,
m∠AEB = (3x + 54)°
⇒m∠AEB = (3(21) + 54)°
⇒m∠AEB = 117°
Therefore, from the given figure m∠AEB = (3x + 54)° and
m∠DEC = (7x -30)°, then the measure of angle AEB is equal to 117°.
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For f(x)=3x^2 – x+5, find the following 2f(–3) – f(4)=
Answer:
33
Step-by-step explanation:
evaluate f(- 3) by substituting x = - 3 into f(x)
f(- 3) = 3(- 3)² - (- 3) + 5 = 3(9) + 9 + 5 = 27 + 14 = 41
evaluate f(4) by substituting x = 4 into f(x)
f(4) = 3(4)² - 4 + 5 = 3(16) + 1 = 48 + 1 = 49
Then
2f(- 3) - f(4) = 2(41) - 49 = 82 - 49 = 33